APPM 2360 Midterm: appm2360fall2016exam1_sol
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Problem 1: (36 points, 6 points each) true/false (answer true if it is always true otherwise answer false) or short answer for the following problems. 100 )p. if p1(t) and p2(t) are both solutions to the y (t) + p(t)y(t) = 2e2t + e3t. Find the function p(t). (short answer) (e) consider the coupled system of equations dx dt dy dt. Find the vertical nullcline(s) of this system. (short answer) (f) for the following di erential equation dy dt. Nd all equilibrium solutions and classify them as stable, unstable or semistable. (short. We may rewrite this equation as y = (t2 1)(y 1). (b) false. Problem 2: (30 points) consider the di erential equation dy dt. Solution: (a: we separate variables and nd that dy y + 1. = 2 sin tdt: integrating both sides, we nd that (2) (3) (4) (8) where c an undetermined constant.
